arXiv research

Defines Killing spinors and bosonic backgrounds in 5D supergravity.

Identifies all perturbative vacua in bosonic string theory.

New decomposable solutions found in 11D supergravity.

We describe the construction of a Lie superalgebra associated to an arbitrary supersymmetric M-theory background, and discuss some examples. We prove that for backgrounds with more than 24 supercharges, the bosonic subalgebra acts locally transitively. In particular, we prove that backgrounds with more than 24 supersym…

We study the algebraic structure of the Killing superalgebra of a supersymmetric background of $11$-dimensional supergravity and show that it is isomorphic to a filtered deformation of a $\mathbb Z$-graded subalgebra of the Poincaré superalgebra. We are able to map the classification problem for highly supersymmetric b…

This paper presents a series of constructions providing eleven-dimensional bosonic supergravity backgrounds. In particular, we treat Lorentzian manifolds given in terms of twisted products of six-dimensional Lorentzian manifolds and five-dimensional Riemannian manifolds. By considering a representative flux 4-form adap…

Derives path integrals for perturbative strings on various backgrounds.

We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plan…

We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.

We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are t…

A common problem in a high energy physics experiment is extracting a signal from a much larger background. Posed as a classification task, there is said to be an imbalance in the number of samples belonging to the signal class versus the number of samples from the background class. In this work we provide a brief overv…

We construct a new class of exact solutions describing spacetimes possessing Lie algebroid symmetry. They are described by generic off-diagaonal 5D metrics embedded in bosonic string gravity and possess nontrivial limits to the Einstein gravity. While we focus on nonholonomic vielbein transforms of the Schwarzschild me…

New method uses machine learning to estimate sensitivity without binning.

We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of $\mathbb{Z}$-graded subalgebras with maximum odd dimension of the $N{=}1$ Poincaré superalgebra in four dimensions. Part of this calcula…

We recover the classification of the maximally supersymmetric bosonic backgrounds of eleven-dimensional supergravity by Lie algebraic means. We classify all filtered deformations of the $\mathbb Z$-graded subalgebras $\mathfrak{h}=\mathfrak{h}_{-2}\oplus\mathfrak{h}_{-1}\oplus\mathfrak{h}_{0}$ of the Poincaré superalge…

We study 4-dimensional higher-derivative conformal higher spin (CHS) fields generalising Weyl graviton and conformal gravitino. They appear, in particular, as "induced" theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. …

We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points generalise the notion of a manifold of holonomy $G_2$, while the constrained ones give ri…

We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form R^{1,9-d} \times M_d, in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-str…

Quantum Proof-of-Work uses boson sampling to secure blockchain consensus.

Researchers create initial data for multiple collapsing boson stars.

We prove the existence of a unique global weak solution to the full bosonic string heat flow from closed Riemannian surfaces to an arbitrary target under smallness conditions on the two-form and the scalar potential. The solution is smooth with the exception of finitely many singular points. Finally, we discuss the con…

Novel Lie-superalgebraic description of superstring dynamics.

This paper mainly aims to establish the well-posedness on time interval $[0,\varepsilon^{-\frac{1}{2}}T]$ of the classical initial problem for the bosonic membrane in the light cone gauge. Here $\varepsilon$ is the small parameter measures the nonlinear effects. In geometric, the bosonic membrane are timelike submanifo…

The model integrates Standard Model bosons into a higher-dimensional spacetime.

We study harmonic maps from surfaces coupled to a scalar and a two-form potential, which arise as critical points of the action of the full bosonic string. We investigate several analytic and geometric properties of these maps and prove an existence result by the heat flow method.

We study the action of the full bosonic string for the domain being two-dimensional Minkowski space and the target a Riemannian manifold. Its critical points couple the wave map equation to a scalar and a two-form potential. Besides investigating their basic features we establish existence results for the latter.

Using probabilistic methods, we first define Liouville quantum field theory on Riemann surfaces of genus $\mathbf{g}\geq 2$ and show that it is a conformal field theory. We use the partition function of Liouville quantum field theory to give a mathematical sense to Polyakov's partition function of noncritical bosonic s…

We show that generalised geometry gives a unified description of bosonic eleven-dimensional supergravity restricted to a $d$-dimensional manifold for all $d\leq7$. The theory is based on an extended tangent space which admits a natural $E_{d(d)} \times \mathbb{R}^+$ action. The bosonic degrees of freedom are unified as…

Sigma models linked to Gross-Neveu models via quiver varieties.

By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization of Thom-Madsen-Tillmann spectra, Adams spectral sequence, and Freed-Hopkins's t…

We calculate the free energy of Coulomb gas systems on Riemann surfaces.

Based on conservation laws for surface layer integrals for critical points of causal variational principles, it is shown how jet spaces can be endowed with an almost-complex structure. We analyze under which conditions the almost-complex structure can be integrated to a canonical complex structure. Combined with the sc…

Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.

Quantum flag manifold σ-models are integrable and satisfy Ricci flow equations.

Positive curvature manifolds from smaller ones using division algebras and geodesic flow.

In this paper we discuss the mechanism of spontaneous symmetry breaking from the point view of vacuum pairs, considered as ground states of a Yang-Mills-Higgs gauge theory. We treat a vacuum as a section in an appropriate bundle that is naturally associated with a minimum of a (general) Higgs potential. Such a vacuum s…

Study on spontaneous symmetry breaking in financial markets using quantum mechanics.

Quantum GBS boosts asset clustering for robust statistical arbitrage portfolios.

We analyze social and economic systems with a hierarchical structure and show that for such systems, it is possible to construct thermostatistics, based on the intermediate Gentile statistics. We show that in social and economic hierarchical systems there are elements that obey the Fermi-Dirac statistics and can be cal…

These notes form part of a lecture course on gauge theory. The material covered is standard in the physics literature, but perhaps less well-known to mathematicians. The purpose of these notes is to make spontaneous symmetry breaking and the Higgs mechanism of mass generation for elementary particles more easily access…

This paper continues the work of our previous paper [8], where we generalize kth-powers of the Euclidean Dirac operator D_x to higher spin spaces in the case the target space is a degree one homogeneous polynomial space. In this paper, we reconsider the generalizations of D_x^3 and D_x^4 to higher spin spaces in the ca…

We reveal connections between RBMs and Bosons, explaining symmetry breaking in their energy landscapes.

We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.

The paper contains a geometrization of the autonomous multi-time Lagrangian function of electrodynamics. We point out that this multi-time Lagrangian function comes from electrodynamics and the theory of bosonic strings.

Defines coherent manifolds and their quantum applications.

We prove a holomorphic residue localization formula for odd holomorphic vector fields on compact complex supermanifolds whose fermionic and bosonic dimensions coincide. Under isolated non-degeneracy hypotheses on the reduced zero set, we give an explicit local residue formula.

Differential forms and symmetric tensors show contrasting singular behaviors in a specific geometric setting.

New principle for supersymmetric localization on Lie groups.